How levels of noise affect phase switching in an inertial majority-vote model
How levels of noise affect phase switching in an inertial majority-vote model lead image
The Ising model, originally developed to describe ferromagnetism, has since been applied to diverse fields like neuroscience, biology, and sociology. It explicates that the state of individual elements — magnetic dipole moments of atomic spins or the activity of neurons, for example — become influenced by the state of their neighbors. By this mechanism, phase transitions can occur.
In Chaos: An Interdisciplinary Journal of Nonlinear Science, a team of physicists report their findings on a non-equilibrium generalization of the Ising model called the inertial majority-vote (IMV) model. The theoretical results, validated by Monte Carlo simulations, show that mean switching time between two symmetric ordered phases varies non-monotonically with the amount of system noise.
In the IMV model, an individual element’s spin-flip probability depends on its state and that of its neighbors. The model displays a discontinuous first-order phase transition exhibited by strong hysteresis behavior as noise is dialed up and down.
The authors used the Wentzel-Kramers-Brillouin approximation for the master equation governing the stochastic spin-flipping processes of the IMV model, which converts it into an effective Hamiltonian system. They calculated mean switching time between phases, with a minimum occurring at the coexisting line where ordered and disordered phases are of the same stability.
Theoretical findings were validated by a rare-event sampling method coupled with Monte Carlo simulation. Because phase switch occurs so infrequently, forward flux sampling method was used to increase the efficiency of the simulations.
According to the authors, the study has important implications for problems involving social systems, such as the emergence of a consensus or spontaneous formation of a common language. Also, Chuansheng Shen says that the findings present a better understanding of the interplay between behavioral inertia and noise in switch phenomena.
Source: “Large deviation induced phase switch in an inertial majority-vote model,” by Hanshuang Chen, Chuansheng Shen, Haifeng Zhang, and Juergen Kurths, Chaos: An Interdisciplinary Journal of Nonlinear Science (2017). The article can be accessed at https://doi.org/10.1063/1.4993520 .
